The solution of the shortest path problem in biochemical systems constitutes an important step for studies of their evolution. In this paper, a linear programming (LP) algorithm for calculating minimal pathway distances in metabolic networks is studied. Minimal pathway distances are identified as the smallest number of metabolic steps separating two enzymes in metabolic pathways. The algorithm deals effectively with circularity and reaction directionality. The applicability of the algorithm is illustrated by calculating the minimal pathway distances for Escherichia coli small molecule metabolism enzymes, and then considering their correlations with genome distance (distance separating two genes on a chromosome) and enzyme function (as characterised by enzyme commission number). The results illustrate the effectiveness of the LP model. In addition, the data confirm that propinquity of genes on the genome implies similarity in function (as determined by co-involvement in the same region of the metabolic network), but suggest that no correlation exists between pathway distance and enzyme function. These findings offer insight into the probable mechanism of pathway evolution.

中文翻译：

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使用路径距离度量通过线性编程对代谢网络进行分析。

生化系统中最短路径问题的解决是研究其进化的重要一步。本文研究了用于计算代谢网络中最小路径距离的线性规划（LP）算法。最小的路径距离被确定为将代谢路径中的两种酶分开的最小数量的代谢步骤。该算法有效地处理了圆度和反应方向性。通过计算大肠杆菌小分子代谢酶的最小途径距离，然后考虑它们与基因组距离（在染色体上分隔两个基因的距离）和酶功能（以酶促数表征）的相关性，来说明该算法的适用性。结果说明了LP模型的有效性。此外，数据证实基因组上基因的预言性暗示功能相似（由共同参与代谢网络的同一区域确定），但表明通路距离与酶功能之间不存在相关性。这些发现提供了途径进化的可能机制的见解。